Cascade amplifier circuit without upper harmonics



Nov. 22, 1938. H. WESSELS 2,137,867

CASCADE AMPLIFIER-CIRCUIT WITHOUT UPPER HARMONIGS Filed Feb. 24, 1956 AAAAAAAA IvIvIvIv AAAAAAA INVENTOR HERMAN WESSELS ATTORNEY atented Nov. 22, 193

UNITED STATES PATENT OFFICE CASCADE AMPLIFIER CIRCUIT WITHOUT UPPER HARMONICS Application February 24, 1936, Serial No. 65,246 In Germany March 5, 1935 1 Claim.

As is known, nonlinear distortions in transmission systems of any type can be compensated in that a system presenting upper harmonics is so connected with a second system having upper harmonics that the upper harmonics compensate each other. To this end, to a tube circuit a second tube circuit may for instance be connected which contains a tube whose characteristic represents the mirror image of the characteristic of the first tube, or two tubes having the same characteristic can be used whereby however the circuit must be such that the input voltage of the second tube is displaced in phase at The invention is based upon the last mentioned suggestion. Previous attempts have been made in producing such a circuit, but it was thereby assumed that the characteristic of the tubes used would always follow the same mathematical law, and that furthermore almost the same working point would have to be chosen, and that finally the quotient of load resistance and internal resistance of the first tube would have to be lower than that of the second tube.

The invention is worked out with particular regard to the teaching that it is of first importance to compensate the second harmonics and that the higher harmonics can by additional consideration in the choice of the working point, be easily reduced to such a value that they no longer disturb the transmission.

The single figure of the drawing shows a twostage amplifier of conventional type (although it will be understood that the invention is not limited to a particular number of stages) which may be operated in accordance with the invention if the steepness and the coupling organs are so chosen that the following equation will be fulfilled:

l z Rai i z stants of the second tube. In matching the end tube with the consumer in order to avoid reflexions and to utilize the end tube as favorably as possible, the equation assumes the following simplified form:

i-Rmsrn It is obvious that a proper choice of the quantities involved will result in satisfying this equa tion, and it will be shown further on that the satisfying of this equation is the condition for eliminating second harmonic distortion in the case where the last tubes impedance is matched by its load impedance. In contrast to this conclusion, it was thought in the prior art that in order to eliminate second harmonic distortion in a circuit of the type here considered it would be necessary to sacrifice a proper matching of the impedances of the load and of the last tube.

Very small upper harmonics can thereby be maintained inasmuch as the working point of a given tube characteristic can be so selected that the expression T becomes as small as possible.

The drawing shows a circuit of a cascade amplifier in accordance with the invention, in connection with which the above stated relation will now be derived in detail.

At the grid of the first tube a purely sinusoidal voltage is assumed namely:

ug1=Ug1 sin to t, (1)

it being the instantaneous value of grid voltage, and U being the amplitude. from which follows the resulting control voltage expressed in terms of the instantaneous grid voltage, plate resistance and load resistance:

It is this voltage list which when multiplied by the steepness S, commonly called mutual conductance or transconductance, gives the alternating plate current. For thechosen working point of the first tube there follows:

ia1=f(ust1) f(Ustl sin to t) (3) In developing the Equation (3) according to Taylors theorem (see Barkhausen Lehrbuch der Elektronen Roehren 2nd volume, Verstaerker, 4th edition, page 57, Formula 51) there will be obtained by neglecting the D. C. portion and the quantities of an order greater than the second order:

mental for the plate resistance Ral.

1 "z 1 stl is the amplitude of the amplified second harmonics related to the plate resistance Ra1='0.

Since however, at finite R31 an anode reaction occurs also for the second harmonics, the actually appearing amplitude of the second harmonics (Barkhausen pages 58-59) is:

and hence according to Equation (1) cosZwt-l- ...(6)

By inserting this value in Equation (6) the equation reads:

This equation represents the anode current in produced by the grid potential UgI- The alternating grid potential of the second tube u is given for R,,))R by the equation:

and' in co'nsideringthe Equation ('7) it is given by the equation:

azm

"The alternating grid potential ugZ forms two parts, namely the fundamental wave given by 14;: (w) and the second harmonics represented by 114%2 (2w).

The amplification of the alternating grid po- U sin w H- tential "M2 by the second tube will be separately treated according to the parts ug2 (w) and u z (2w) in the following course of the calculation.

For the part ug2 (w) there follows analogous to Equation (7):

1 -5U,2 9 cos 2 w t whereby according to Equation (9) Ua w :s1 o

The amplitude of the plate current of the second harmonics produced in the second tube by the fundamental wave u z ((0) will be according to Equations (10, 11):

Ia2(2w/ )=siT2-- 2 Ruz oz, ..(1z)

Rfl R1-2 For the grid voltage part u e (201) representing the second harmonics, substantially only the linear amplification need be considered since owing to the'smallness of this part, the higher harmonics determined thereby are of an order that 'is smaller than the second order. Therefore, for the amplification of 'llg2 (2w) an anode current is obtained:

i 2w =s2-1 -U,2 2w cos 2 m t (13) 1?) so that according to Equation (9):

g2( w)= 1M 2 4) The amplitude of the plate current of the second harmonics produced in the second tube by the second harmonics u z (2w) will be in accordance with Equations (13) and (14):

gt} 3 aZ n 12) From Equation (12) and (15) there follows for the resulting amplitude of' the second harmonics of the plate current 1'32:

I CZw)=I (2w/2w)+I (2w/w)= R T 111 ;1 -f+ 4 R51 m (16) wan n iz Due to the phase displacement of between the two parts Iaz (2w/w) and Ia2(2w/2w), also indicated by the different "signs of the amplitudes, the second harmonics of the plate current can be made to disappear. This occurs when the quantity -in the brackets becomes equal to zero in other words the'following condition of the invention is fulfilled, namely:

This condition'will in general be fulfilled for the disappearance of the second harmonics of a resistance-capacity coupled cascade amplifier. In matching in accordance with a further feature of the invention, the output of the cascade with the consumer the Formula (1'?) assumes the simplified expression:

( it-I) As tests have shown, an amplifier circuit can be produced by the use of the idea of the invention which has a noise factor of less than 0.05%. The direct grid potential which determines the working point and hence the steepness S may in this case even fluctuate within the limits of :5%, a tolerance not even utilized in ordinary grid batteries.

The application of the invention moreover, is not limited to the circuit shown in the drawing. In like manner it may be utilized also in cascade circuits with more than two tubes. Furthermore, two cascades as shown in the figure may abo be combined to a push-pull circuit.

What I claim is:

A cascade amplifier comprising a first tube, a coupling resistance Ra1 in the anode alternating current path of the first tube, a second tube coupled to the first tube and fed with the entire voltage developed across said coupling resistance, a load resistance Raz in the anode circuit of the second tube, the resistance Ral satisfying the equation 152 n f z al R412 a e) s) where S1, S2 are the rates of change of plate current with respect to grid voltage of the first and second tubes respectively, T1, T2 are the rates of change of S with respect to grid voltage of the first and second tubes respectively and Ru, R12 are the internal plate resistances of the first and second tubes respectively, whereby the output of the second tube is substantially free of second harmonics of the signals applied to the input of said amplifier.

HERMANN WESSELS. 

